OS X Disk Utility missing options to erase free disk space

Erasing free disk space is an easy (albeit not quick) way to help
prevent the recovery of files you have erased from your system.
Conventionally when files are deleted from storage device, the system
only removes their entries from the file system's directory, thereby
flagging blocks containing the data as being free to use. While this
offers a quick way to delete files from the drive, the data is
technically still intact on disk and thereby leaves open the possibility
for recovery using special software.
To prevent this from happening, one option that Apple has offered in
OS X is to erase the free disk space using Disk Utility. This option
writes zeros to the unused portions of the drive and overwrites any
previously deleted files.
This option makes it nearly impossible for the drive's heads to be
used for reading any residual magnetism patterns and recover files.
Instead, any remote possibility of data recovery would require
dissection of the drive and the use of specialized equipment that can
detect residual magnetism.

Even with using specialized equipment, such a procedure would only
increase the slim possibility of data recovery, so using Disk Utility to
erase free space does have its security benefits; however, if you have
purchased a new
Mac system or upgraded your hard drive, then you may find Disk Utility no longer offers this as an option.
If you find this is the case with your system, and Disk Utility only
shows the Erase Free Space option as being grayed out, then it is likely
the reason is because your Mac is using an SSD as its primary storage
device.
Solid-state technology has the benefit of being exceptionally fast;
however, the storage blocks in the NAND memory chips have a finite
number of write operations that can be performed before they will no
longer hold data reliably. To combat this problem, SSD manufacturers
implement techniques called "wear leveling," which distribute write
operations through the available memory chips and extend the life of the
drive by ensuring they all get used evenly.
If you were to erase the free disk space on an SSD, you would force
the system to unnecessarily write not only to locations where data
previously was stored, but also to fresh locations on the drive that
have not yet been used. Overall this would just wear out the SSD faster
and result in a premature degradation of the drive's performance.
In addition, such an operation might cause your system to no longer
work properly. On some SSD drives, once data is written the system will
need to perform operations to free it. These procedure can take a little
longer than both the read and the write operations themselves, and in
the mean time the drive might report to the system that it no longer has
any space available to store data, which can result in your system
booting slowly or not being able to boot at all.
To avoid these problems and to keep your SSD as fresh as possible for
the long term, Apple has disabled Disk Utility's secure erase option
for some SSD devices.
Keep in mind that this only affects internal SSDs, and may only be
the case for certain SSD devices (particularly those made by Apple).
Therefore, if you have a special SSD setup on your system, then the
option to erase free space might still be available. However, you would
benefit from avoiding it.
Furthermore, even if the system prevents you from using the erase
free disk space feature, the Finder's Secure Erase option that
overwrites deleted files with random data may still be available.
However, as with the option to erase free space, it may be best to avoid
this feature because the multiple writes it performs will reduce your
SSD's lifetime.
If you wish to keep files secure on your SSD device, then the best
option to use is encryption. With encryption, the system keeps the data
scrambled unless a proper password or decryption key is provided, so to
securely delete files you just need to delete the decryption keys or
password to access them, and for all intents and purposes the files will
be irrecoverably deleted.
Apple provides two options for encrypting files in OS X. The first is to use the whole-disk FileVault technology, and the second is to use disk images as encrypted wrappers to house subsets of files instead of encrypting everything.